Properties

Label 637.2.k.g.569.5
Level $637$
Weight $2$
Character 637.569
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.5
Root \(1.40744 + 0.138282i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.g.459.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.27656i q^{2} +(-0.583963 + 1.01145i) q^{3} +0.370384 q^{4} +(-1.57173 - 0.907437i) q^{5} +(-1.29118 - 0.745466i) q^{6} +3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +O(q^{10})\) \(q+1.27656i q^{2} +(-0.583963 + 1.01145i) q^{3} +0.370384 q^{4} +(-1.57173 - 0.907437i) q^{5} +(-1.29118 - 0.745466i) q^{6} +3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +(1.15840 - 2.00641i) q^{10} +(2.40625 + 1.38925i) q^{11} +(-0.216290 + 0.374626i) q^{12} +(3.58305 + 0.402155i) q^{13} +(1.83566 - 1.05982i) q^{15} -3.12205 q^{16} +2.74396 q^{17} +(-1.80860 + 1.04420i) q^{18} +(-5.08351 + 2.93497i) q^{19} +(-0.582143 - 0.336100i) q^{20} +(-1.77346 + 3.07173i) q^{22} -6.99909 q^{23} +(-3.06060 - 1.76704i) q^{24} +(-0.853117 - 1.47764i) q^{25} +(-0.513376 + 4.57400i) q^{26} -5.41444 q^{27} +(1.75806 + 3.04505i) q^{29} +(1.35293 + 2.34334i) q^{30} +(-1.79004 + 1.03348i) q^{31} +2.06640i q^{32} +(-2.81031 + 1.62254i) q^{33} +3.50284i q^{34} +(0.302965 + 0.524751i) q^{36} +1.74302i q^{37} +(-3.74667 - 6.48942i) q^{38} +(-2.49913 + 3.38925i) q^{39} +(2.74586 - 4.75596i) q^{40} +(-5.51406 + 3.18355i) q^{41} +(4.55195 - 7.88422i) q^{43} +(0.891235 + 0.514555i) q^{44} -2.96904i q^{45} -8.93479i q^{46} +(5.76714 + 3.32966i) q^{47} +(1.82316 - 3.15780i) q^{48} +(1.88631 - 1.08906i) q^{50} +(-1.60237 + 2.77539i) q^{51} +(1.32711 + 0.148952i) q^{52} +(5.24396 + 9.08280i) q^{53} -6.91188i q^{54} +(-2.52131 - 4.36703i) q^{55} -6.85564i q^{57} +(-3.88720 + 2.24427i) q^{58} +3.07396i q^{59} +(0.679899 - 0.392540i) q^{60} +(0.540892 + 0.936853i) q^{61} +(-1.31931 - 2.28511i) q^{62} -8.88199 q^{64} +(-5.26665 - 3.88347i) q^{65} +(-2.07127 - 3.58755i) q^{66} +(-4.34568 - 2.50898i) q^{67} +1.01632 q^{68} +(4.08721 - 7.07925i) q^{69} +(2.35453 + 1.35939i) q^{71} +(-4.28709 + 2.47515i) q^{72} +(6.64426 - 3.83607i) q^{73} -2.22508 q^{74} +1.99275 q^{75} +(-1.88285 + 1.08706i) q^{76} +(-4.32659 - 3.19030i) q^{78} +(7.86993 - 13.6311i) q^{79} +(4.90700 + 2.83306i) q^{80} +(0.707906 - 1.22613i) q^{81} +(-4.06400 - 7.03905i) q^{82} -7.97408i q^{83} +(-4.31275 - 2.48997i) q^{85} +(10.0647 + 5.81086i) q^{86} -4.10656 q^{87} +(-4.20379 + 7.28117i) q^{88} +16.0640i q^{89} +3.79017 q^{90} -2.59235 q^{92} -2.41406i q^{93} +(-4.25052 + 7.36212i) q^{94} +10.6532 q^{95} +(-2.09007 - 1.20670i) q^{96} +(12.3209 + 7.11347i) q^{97} +4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27656i 0.902667i 0.892355 + 0.451334i \(0.149052\pi\)
−0.892355 + 0.451334i \(0.850948\pi\)
\(3\) −0.583963 + 1.01145i −0.337151 + 0.583963i −0.983896 0.178744i \(-0.942797\pi\)
0.646745 + 0.762707i \(0.276130\pi\)
\(4\) 0.370384 0.185192
\(5\) −1.57173 0.907437i −0.702897 0.405818i 0.105528 0.994416i \(-0.466347\pi\)
−0.808426 + 0.588598i \(0.799680\pi\)
\(6\) −1.29118 0.745466i −0.527124 0.304335i
\(7\) 0 0
\(8\) 3.02595i 1.06983i
\(9\) 0.817975 + 1.41677i 0.272658 + 0.472258i
\(10\) 1.15840 2.00641i 0.366319 0.634482i
\(11\) 2.40625 + 1.38925i 0.725510 + 0.418874i 0.816777 0.576953i \(-0.195758\pi\)
−0.0912671 + 0.995826i \(0.529092\pi\)
\(12\) −0.216290 + 0.374626i −0.0624377 + 0.108145i
\(13\) 3.58305 + 0.402155i 0.993760 + 0.111538i
\(14\) 0 0
\(15\) 1.83566 1.05982i 0.473965 0.273644i
\(16\) −3.12205 −0.780512
\(17\) 2.74396 0.665508 0.332754 0.943014i \(-0.392022\pi\)
0.332754 + 0.943014i \(0.392022\pi\)
\(18\) −1.80860 + 1.04420i −0.426292 + 0.246120i
\(19\) −5.08351 + 2.93497i −1.16624 + 0.673327i −0.952791 0.303628i \(-0.901802\pi\)
−0.213446 + 0.976955i \(0.568469\pi\)
\(20\) −0.582143 0.336100i −0.130171 0.0751543i
\(21\) 0 0
\(22\) −1.77346 + 3.07173i −0.378103 + 0.654894i
\(23\) −6.99909 −1.45941 −0.729706 0.683761i \(-0.760343\pi\)
−0.729706 + 0.683761i \(0.760343\pi\)
\(24\) −3.06060 1.76704i −0.624743 0.360696i
\(25\) −0.853117 1.47764i −0.170623 0.295528i
\(26\) −0.513376 + 4.57400i −0.100681 + 0.897035i
\(27\) −5.41444 −1.04201
\(28\) 0 0
\(29\) 1.75806 + 3.04505i 0.326463 + 0.565451i 0.981807 0.189879i \(-0.0608097\pi\)
−0.655344 + 0.755330i \(0.727476\pi\)
\(30\) 1.35293 + 2.34334i 0.247009 + 0.427833i
\(31\) −1.79004 + 1.03348i −0.321501 + 0.185619i −0.652062 0.758166i \(-0.726096\pi\)
0.330560 + 0.943785i \(0.392762\pi\)
\(32\) 2.06640i 0.365292i
\(33\) −2.81031 + 1.62254i −0.489213 + 0.282447i
\(34\) 3.50284i 0.600732i
\(35\) 0 0
\(36\) 0.302965 + 0.524751i 0.0504942 + 0.0874585i
\(37\) 1.74302i 0.286551i 0.989683 + 0.143276i \(0.0457635\pi\)
−0.989683 + 0.143276i \(0.954236\pi\)
\(38\) −3.74667 6.48942i −0.607790 1.05272i
\(39\) −2.49913 + 3.38925i −0.400181 + 0.542714i
\(40\) 2.74586 4.75596i 0.434158 0.751984i
\(41\) −5.51406 + 3.18355i −0.861152 + 0.497186i −0.864398 0.502808i \(-0.832300\pi\)
0.00324599 + 0.999995i \(0.498967\pi\)
\(42\) 0 0
\(43\) 4.55195 7.88422i 0.694167 1.20233i −0.276294 0.961073i \(-0.589106\pi\)
0.970461 0.241259i \(-0.0775603\pi\)
\(44\) 0.891235 + 0.514555i 0.134359 + 0.0775721i
\(45\) 2.96904i 0.442599i
\(46\) 8.93479i 1.31736i
\(47\) 5.76714 + 3.32966i 0.841224 + 0.485681i 0.857680 0.514184i \(-0.171905\pi\)
−0.0164563 + 0.999865i \(0.505238\pi\)
\(48\) 1.82316 3.15780i 0.263150 0.455790i
\(49\) 0 0
\(50\) 1.88631 1.08906i 0.266764 0.154016i
\(51\) −1.60237 + 2.77539i −0.224377 + 0.388632i
\(52\) 1.32711 + 0.148952i 0.184037 + 0.0206559i
\(53\) 5.24396 + 9.08280i 0.720313 + 1.24762i 0.960874 + 0.276985i \(0.0893352\pi\)
−0.240561 + 0.970634i \(0.577331\pi\)
\(54\) 6.91188i 0.940588i
\(55\) −2.52131 4.36703i −0.339973 0.588850i
\(56\) 0 0
\(57\) 6.85564i 0.908052i
\(58\) −3.88720 + 2.24427i −0.510414 + 0.294688i
\(59\) 3.07396i 0.400195i 0.979776 + 0.200097i \(0.0641259\pi\)
−0.979776 + 0.200097i \(0.935874\pi\)
\(60\) 0.679899 0.392540i 0.0877746 0.0506767i
\(61\) 0.540892 + 0.936853i 0.0692541 + 0.119952i 0.898573 0.438824i \(-0.144605\pi\)
−0.829319 + 0.558775i \(0.811271\pi\)
\(62\) −1.31931 2.28511i −0.167552 0.290209i
\(63\) 0 0
\(64\) −8.88199 −1.11025
\(65\) −5.26665 3.88347i −0.653248 0.481685i
\(66\) −2.07127 3.58755i −0.254956 0.441596i
\(67\) −4.34568 2.50898i −0.530910 0.306521i 0.210477 0.977599i \(-0.432498\pi\)
−0.741387 + 0.671078i \(0.765832\pi\)
\(68\) 1.01632 0.123247
\(69\) 4.08721 7.07925i 0.492042 0.852242i
\(70\) 0 0
\(71\) 2.35453 + 1.35939i 0.279431 + 0.161330i 0.633166 0.774016i \(-0.281755\pi\)
−0.353735 + 0.935346i \(0.615088\pi\)
\(72\) −4.28709 + 2.47515i −0.505238 + 0.291699i
\(73\) 6.64426 3.83607i 0.777652 0.448978i −0.0579454 0.998320i \(-0.518455\pi\)
0.835598 + 0.549342i \(0.185122\pi\)
\(74\) −2.22508 −0.258660
\(75\) 1.99275 0.230103
\(76\) −1.88285 + 1.08706i −0.215978 + 0.124695i
\(77\) 0 0
\(78\) −4.32659 3.19030i −0.489890 0.361230i
\(79\) 7.86993 13.6311i 0.885436 1.53362i 0.0402236 0.999191i \(-0.487193\pi\)
0.845213 0.534430i \(-0.179474\pi\)
\(80\) 4.90700 + 2.83306i 0.548620 + 0.316746i
\(81\) 0.707906 1.22613i 0.0786563 0.136237i
\(82\) −4.06400 7.03905i −0.448794 0.777333i
\(83\) 7.97408i 0.875269i −0.899153 0.437635i \(-0.855816\pi\)
0.899153 0.437635i \(-0.144184\pi\)
\(84\) 0 0
\(85\) −4.31275 2.48997i −0.467784 0.270075i
\(86\) 10.0647 + 5.81086i 1.08531 + 0.626601i
\(87\) −4.10656 −0.440270
\(88\) −4.20379 + 7.28117i −0.448125 + 0.776176i
\(89\) 16.0640i 1.70278i 0.524537 + 0.851388i \(0.324239\pi\)
−0.524537 + 0.851388i \(0.675761\pi\)
\(90\) 3.79017 0.399519
\(91\) 0 0
\(92\) −2.59235 −0.270271
\(93\) 2.41406i 0.250326i
\(94\) −4.25052 + 7.36212i −0.438408 + 0.759345i
\(95\) 10.6532 1.09299
\(96\) −2.09007 1.20670i −0.213317 0.123158i
\(97\) 12.3209 + 7.11347i 1.25100 + 0.722263i 0.971307 0.237827i \(-0.0764353\pi\)
0.279689 + 0.960091i \(0.409769\pi\)
\(98\) 0 0
\(99\) 4.54548i 0.456838i
\(100\) −0.315981 0.547295i −0.0315981 0.0547295i
\(101\) 0.0365612 0.0633259i 0.00363798 0.00630117i −0.864201 0.503147i \(-0.832175\pi\)
0.867839 + 0.496846i \(0.165509\pi\)
\(102\) −3.54296 2.04553i −0.350805 0.202537i
\(103\) 6.45980 11.1887i 0.636503 1.10245i −0.349692 0.936865i \(-0.613714\pi\)
0.986195 0.165590i \(-0.0529529\pi\)
\(104\) −1.21690 + 10.8421i −0.119327 + 1.06316i
\(105\) 0 0
\(106\) −11.5948 + 6.69425i −1.12618 + 0.650203i
\(107\) 4.00855 0.387521 0.193761 0.981049i \(-0.437932\pi\)
0.193761 + 0.981049i \(0.437932\pi\)
\(108\) −2.00542 −0.192972
\(109\) −1.71984 + 0.992947i −0.164730 + 0.0951071i −0.580099 0.814546i \(-0.696986\pi\)
0.415368 + 0.909653i \(0.363653\pi\)
\(110\) 5.57479 3.21861i 0.531536 0.306882i
\(111\) −1.76299 1.01786i −0.167335 0.0966110i
\(112\) 0 0
\(113\) 5.28711 9.15754i 0.497369 0.861469i −0.502626 0.864504i \(-0.667633\pi\)
0.999995 + 0.00303506i \(0.000966090\pi\)
\(114\) 8.75166 0.819668
\(115\) 11.0007 + 6.35123i 1.02582 + 0.592256i
\(116\) 0.651157 + 1.12784i 0.0604584 + 0.104717i
\(117\) 2.36109 + 5.40533i 0.218283 + 0.499723i
\(118\) −3.92410 −0.361243
\(119\) 0 0
\(120\) 3.20695 + 5.55461i 0.292753 + 0.507064i
\(121\) −1.63999 2.84054i −0.149090 0.258231i
\(122\) −1.19595 + 0.690483i −0.108276 + 0.0625134i
\(123\) 7.43629i 0.670507i
\(124\) −0.663004 + 0.382786i −0.0595395 + 0.0343752i
\(125\) 12.1710i 1.08860i
\(126\) 0 0
\(127\) 5.63478 + 9.75972i 0.500006 + 0.866035i 1.00000 6.53271e-6i \(2.07943e-6\pi\)
−0.499994 + 0.866029i \(0.666665\pi\)
\(128\) 7.20562i 0.636893i
\(129\) 5.31634 + 9.20818i 0.468078 + 0.810735i
\(130\) 4.95750 6.72322i 0.434801 0.589665i
\(131\) 1.53241 2.65421i 0.133887 0.231899i −0.791285 0.611448i \(-0.790587\pi\)
0.925172 + 0.379549i \(0.123921\pi\)
\(132\) −1.04090 + 0.600962i −0.0905984 + 0.0523070i
\(133\) 0 0
\(134\) 3.20288 5.54754i 0.276686 0.479235i
\(135\) 8.51002 + 4.91326i 0.732426 + 0.422867i
\(136\) 8.30308i 0.711983i
\(137\) 21.8830i 1.86959i −0.355185 0.934796i \(-0.615582\pi\)
0.355185 0.934796i \(-0.384418\pi\)
\(138\) 9.03712 + 5.21758i 0.769291 + 0.444150i
\(139\) 5.53535 9.58750i 0.469502 0.813201i −0.529890 0.848066i \(-0.677767\pi\)
0.999392 + 0.0348652i \(0.0111002\pi\)
\(140\) 0 0
\(141\) −6.73559 + 3.88879i −0.567239 + 0.327495i
\(142\) −1.73534 + 3.00570i −0.145627 + 0.252233i
\(143\) 8.06301 + 5.94543i 0.674263 + 0.497182i
\(144\) −2.55376 4.42324i −0.212813 0.368603i
\(145\) 6.38131i 0.529939i
\(146\) 4.89699 + 8.48183i 0.405277 + 0.701961i
\(147\) 0 0
\(148\) 0.645588i 0.0530670i
\(149\) 1.99824 1.15369i 0.163702 0.0945136i −0.415911 0.909406i \(-0.636537\pi\)
0.579613 + 0.814892i \(0.303204\pi\)
\(150\) 2.54388i 0.207707i
\(151\) −17.8538 + 10.3079i −1.45292 + 0.838845i −0.998646 0.0520168i \(-0.983435\pi\)
−0.454275 + 0.890861i \(0.650102\pi\)
\(152\) −8.88105 15.3824i −0.720348 1.24768i
\(153\) 2.24449 + 3.88757i 0.181456 + 0.314292i
\(154\) 0 0
\(155\) 3.75128 0.301310
\(156\) −0.925638 + 1.25532i −0.0741103 + 0.100506i
\(157\) 1.44824 + 2.50843i 0.115582 + 0.200194i 0.918012 0.396552i \(-0.129793\pi\)
−0.802430 + 0.596746i \(0.796460\pi\)
\(158\) 17.4010 + 10.0465i 1.38435 + 0.799254i
\(159\) −12.2491 −0.971417
\(160\) 1.87513 3.24782i 0.148242 0.256763i
\(161\) 0 0
\(162\) 1.56523 + 0.903688i 0.122976 + 0.0710004i
\(163\) 20.2944 11.7170i 1.58958 0.917743i 0.596201 0.802835i \(-0.296676\pi\)
0.993376 0.114907i \(-0.0366571\pi\)
\(164\) −2.04232 + 1.17913i −0.159478 + 0.0920750i
\(165\) 5.88939 0.458489
\(166\) 10.1794 0.790077
\(167\) −6.58349 + 3.80098i −0.509446 + 0.294129i −0.732606 0.680653i \(-0.761696\pi\)
0.223160 + 0.974782i \(0.428363\pi\)
\(168\) 0 0
\(169\) 12.6765 + 2.88188i 0.975119 + 0.221683i
\(170\) 3.17861 5.50551i 0.243788 0.422253i
\(171\) −8.31637 4.80146i −0.635969 0.367177i
\(172\) 1.68597 2.92019i 0.128554 0.222662i
\(173\) −2.69861 4.67412i −0.205171 0.355367i 0.745016 0.667047i \(-0.232442\pi\)
−0.950187 + 0.311679i \(0.899108\pi\)
\(174\) 5.24229i 0.397417i
\(175\) 0 0
\(176\) −7.51241 4.33729i −0.566269 0.326936i
\(177\) −3.10916 1.79508i −0.233699 0.134926i
\(178\) −20.5067 −1.53704
\(179\) −6.14571 + 10.6447i −0.459352 + 0.795621i −0.998927 0.0463168i \(-0.985252\pi\)
0.539575 + 0.841938i \(0.318585\pi\)
\(180\) 1.09969i 0.0819658i
\(181\) 21.8525 1.62428 0.812140 0.583463i \(-0.198303\pi\)
0.812140 + 0.583463i \(0.198303\pi\)
\(182\) 0 0
\(183\) −1.26344 −0.0933964
\(184\) 21.1789i 1.56133i
\(185\) 1.58168 2.73956i 0.116288 0.201416i
\(186\) 3.08170 0.225961
\(187\) 6.60264 + 3.81204i 0.482833 + 0.278764i
\(188\) 2.13606 + 1.23325i 0.155788 + 0.0899442i
\(189\) 0 0
\(190\) 13.5995i 0.986609i
\(191\) −1.37858 2.38777i −0.0997507 0.172773i 0.811831 0.583893i \(-0.198471\pi\)
−0.911581 + 0.411120i \(0.865138\pi\)
\(192\) 5.18675 8.98371i 0.374321 0.648344i
\(193\) −11.2491 6.49467i −0.809728 0.467497i 0.0371334 0.999310i \(-0.488177\pi\)
−0.846861 + 0.531814i \(0.821511\pi\)
\(194\) −9.08080 + 15.7284i −0.651963 + 1.12923i
\(195\) 7.00347 3.05917i 0.501529 0.219071i
\(196\) 0 0
\(197\) 16.4772 9.51312i 1.17395 0.677781i 0.219344 0.975648i \(-0.429608\pi\)
0.954608 + 0.297866i \(0.0962749\pi\)
\(198\) −5.80259 −0.412372
\(199\) −20.0317 −1.42001 −0.710006 0.704195i \(-0.751308\pi\)
−0.710006 + 0.704195i \(0.751308\pi\)
\(200\) 4.47127 2.58149i 0.316166 0.182539i
\(201\) 5.07543 2.93030i 0.357993 0.206688i
\(202\) 0.0808396 + 0.0466728i 0.00568785 + 0.00328388i
\(203\) 0 0
\(204\) −0.593492 + 1.02796i −0.0415528 + 0.0719715i
\(205\) 11.5555 0.807069
\(206\) 14.2831 + 8.24634i 0.995150 + 0.574550i
\(207\) −5.72509 9.91614i −0.397921 0.689219i
\(208\) −11.1865 1.25555i −0.775642 0.0870564i
\(209\) −16.3096 −1.12816
\(210\) 0 0
\(211\) −5.00015 8.66052i −0.344225 0.596215i 0.640988 0.767551i \(-0.278525\pi\)
−0.985213 + 0.171336i \(0.945192\pi\)
\(212\) 1.94228 + 3.36413i 0.133396 + 0.231049i
\(213\) −2.74991 + 1.58766i −0.188421 + 0.108785i
\(214\) 5.11717i 0.349802i
\(215\) −14.3089 + 8.26122i −0.975856 + 0.563411i
\(216\) 16.3838i 1.11478i
\(217\) 0 0
\(218\) −1.26756 2.19548i −0.0858501 0.148697i
\(219\) 8.96048i 0.605493i
\(220\) −0.933852 1.61748i −0.0629603 0.109050i
\(221\) 9.83175 + 1.10350i 0.661355 + 0.0742292i
\(222\) 1.29936 2.25056i 0.0872076 0.151048i
\(223\) −7.25954 + 4.19130i −0.486135 + 0.280670i −0.722970 0.690880i \(-0.757223\pi\)
0.236835 + 0.971550i \(0.423890\pi\)
\(224\) 0 0
\(225\) 1.39566 2.41735i 0.0930439 0.161157i
\(226\) 11.6902 + 6.74933i 0.777620 + 0.448959i
\(227\) 0.919719i 0.0610439i −0.999534 0.0305220i \(-0.990283\pi\)
0.999534 0.0305220i \(-0.00971695\pi\)
\(228\) 2.53922i 0.168164i
\(229\) 21.3222 + 12.3104i 1.40901 + 0.813494i 0.995293 0.0969108i \(-0.0308962\pi\)
0.413719 + 0.910404i \(0.364229\pi\)
\(230\) −8.10776 + 14.0430i −0.534610 + 0.925971i
\(231\) 0 0
\(232\) −9.21415 + 5.31979i −0.604939 + 0.349261i
\(233\) −8.63847 + 14.9623i −0.565925 + 0.980211i 0.431038 + 0.902334i \(0.358148\pi\)
−0.996963 + 0.0778773i \(0.975186\pi\)
\(234\) −6.90025 + 3.01408i −0.451084 + 0.197036i
\(235\) −6.04291 10.4666i −0.394196 0.682767i
\(236\) 1.13854i 0.0741129i
\(237\) 9.19149 + 15.9201i 0.597051 + 1.03412i
\(238\) 0 0
\(239\) 14.4828i 0.936816i 0.883512 + 0.468408i \(0.155172\pi\)
−0.883512 + 0.468408i \(0.844828\pi\)
\(240\) −5.73101 + 3.30880i −0.369935 + 0.213582i
\(241\) 8.43441i 0.543308i −0.962395 0.271654i \(-0.912429\pi\)
0.962395 0.271654i \(-0.0875706\pi\)
\(242\) 3.62614 2.09355i 0.233097 0.134579i
\(243\) −7.29488 12.6351i −0.467967 0.810543i
\(244\) 0.200338 + 0.346995i 0.0128253 + 0.0222141i
\(245\) 0 0
\(246\) 9.49290 0.605245
\(247\) −19.3948 + 8.47178i −1.23406 + 0.539046i
\(248\) −3.12726 5.41658i −0.198581 0.343953i
\(249\) 8.06541 + 4.65657i 0.511124 + 0.295098i
\(250\) −15.5370 −0.982647
\(251\) 7.33631 12.7069i 0.463064 0.802050i −0.536048 0.844188i \(-0.680083\pi\)
0.999112 + 0.0421373i \(0.0134167\pi\)
\(252\) 0 0
\(253\) −16.8415 9.72346i −1.05882 0.611309i
\(254\) −12.4589 + 7.19315i −0.781742 + 0.451339i
\(255\) 5.03697 2.90810i 0.315427 0.182112i
\(256\) −8.56553 −0.535346
\(257\) 29.3286 1.82947 0.914733 0.404059i \(-0.132401\pi\)
0.914733 + 0.404059i \(0.132401\pi\)
\(258\) −11.7548 + 6.78665i −0.731824 + 0.422519i
\(259\) 0 0
\(260\) −1.95068 1.43838i −0.120976 0.0892043i
\(261\) −2.87610 + 4.98155i −0.178026 + 0.308350i
\(262\) 3.38826 + 1.95622i 0.209328 + 0.120855i
\(263\) −9.95747 + 17.2468i −0.614004 + 1.06349i 0.376555 + 0.926394i \(0.377109\pi\)
−0.990558 + 0.137091i \(0.956225\pi\)
\(264\) −4.90971 8.50386i −0.302172 0.523377i
\(265\) 19.0342i 1.16926i
\(266\) 0 0
\(267\) −16.2479 9.38075i −0.994357 0.574092i
\(268\) −1.60957 0.929287i −0.0983203 0.0567652i
\(269\) 22.3250 1.36118 0.680589 0.732666i \(-0.261724\pi\)
0.680589 + 0.732666i \(0.261724\pi\)
\(270\) −6.27210 + 10.8636i −0.381708 + 0.661137i
\(271\) 9.39988i 0.571002i 0.958378 + 0.285501i \(0.0921600\pi\)
−0.958378 + 0.285501i \(0.907840\pi\)
\(272\) −8.56677 −0.519437
\(273\) 0 0
\(274\) 27.9351 1.68762
\(275\) 4.74076i 0.285879i
\(276\) 1.51384 2.62204i 0.0911223 0.157828i
\(277\) 14.3427 0.861767 0.430883 0.902408i \(-0.358202\pi\)
0.430883 + 0.902408i \(0.358202\pi\)
\(278\) 12.2391 + 7.06622i 0.734050 + 0.423804i
\(279\) −2.92842 1.69073i −0.175320 0.101221i
\(280\) 0 0
\(281\) 0.0988416i 0.00589640i 0.999996 + 0.00294820i \(0.000938442\pi\)
−0.999996 + 0.00294820i \(0.999062\pi\)
\(282\) −4.96429 8.59841i −0.295619 0.512028i
\(283\) 0.310336 0.537518i 0.0184476 0.0319521i −0.856654 0.515891i \(-0.827461\pi\)
0.875102 + 0.483939i \(0.160794\pi\)
\(284\) 0.872079 + 0.503495i 0.0517484 + 0.0298769i
\(285\) −6.22106 + 10.7752i −0.368504 + 0.638267i
\(286\) −7.58972 + 10.2930i −0.448789 + 0.608635i
\(287\) 0 0
\(288\) −2.92763 + 1.69027i −0.172512 + 0.0995998i
\(289\) −9.47069 −0.557099
\(290\) 8.14615 0.478358
\(291\) −14.3899 + 8.30800i −0.843549 + 0.487023i
\(292\) 2.46093 1.42082i 0.144015 0.0831471i
\(293\) −21.5586 12.4469i −1.25947 0.727153i −0.286496 0.958082i \(-0.592490\pi\)
−0.972971 + 0.230928i \(0.925824\pi\)
\(294\) 0 0
\(295\) 2.78942 4.83142i 0.162406 0.281296i
\(296\) −5.27430 −0.306562
\(297\) −13.0285 7.52200i −0.755989 0.436471i
\(298\) 1.47275 + 2.55088i 0.0853143 + 0.147769i
\(299\) −25.0781 2.81472i −1.45031 0.162779i
\(300\) 0.738085 0.0426133
\(301\) 0 0
\(302\) −13.1587 22.7915i −0.757197 1.31150i
\(303\) 0.0427008 + 0.0739599i 0.00245310 + 0.00424889i
\(304\) 15.8710 9.16310i 0.910262 0.525540i
\(305\) 1.96330i 0.112418i
\(306\) −4.96274 + 2.86524i −0.283701 + 0.163795i
\(307\) 9.89767i 0.564890i −0.959284 0.282445i \(-0.908855\pi\)
0.959284 0.282445i \(-0.0911455\pi\)
\(308\) 0 0
\(309\) 7.54456 + 13.0676i 0.429195 + 0.743387i
\(310\) 4.78875i 0.271983i
\(311\) −3.61895 6.26820i −0.205212 0.355437i 0.744988 0.667077i \(-0.232455\pi\)
−0.950200 + 0.311640i \(0.899122\pi\)
\(312\) −10.2557 7.56223i −0.580614 0.428127i
\(313\) 16.3303 28.2849i 0.923043 1.59876i 0.128365 0.991727i \(-0.459027\pi\)
0.794678 0.607031i \(-0.207640\pi\)
\(314\) −3.20217 + 1.84877i −0.180709 + 0.104332i
\(315\) 0 0
\(316\) 2.91490 5.04875i 0.163976 0.284014i
\(317\) −14.8734 8.58718i −0.835375 0.482304i 0.0203143 0.999794i \(-0.493533\pi\)
−0.855690 + 0.517489i \(0.826867\pi\)
\(318\) 15.6368i 0.876866i
\(319\) 9.76951i 0.546987i
\(320\) 13.9601 + 8.05984i 0.780391 + 0.450559i
\(321\) −2.34084 + 4.05446i −0.130653 + 0.226298i
\(322\) 0 0
\(323\) −13.9489 + 8.05342i −0.776140 + 0.448105i
\(324\) 0.262197 0.454139i 0.0145665 0.0252299i
\(325\) −2.46252 5.63756i −0.136596 0.312715i
\(326\) 14.9574 + 25.9071i 0.828416 + 1.43486i
\(327\) 2.31938i 0.128262i
\(328\) −9.63324 16.6853i −0.531907 0.921289i
\(329\) 0 0
\(330\) 7.51819i 0.413863i
\(331\) −17.2633 + 9.96698i −0.948877 + 0.547835i −0.892732 0.450588i \(-0.851214\pi\)
−0.0561454 + 0.998423i \(0.517881\pi\)
\(332\) 2.95347i 0.162093i
\(333\) −2.46947 + 1.42575i −0.135326 + 0.0781306i
\(334\) −4.85219 8.40424i −0.265500 0.459860i
\(335\) 4.55348 + 7.88687i 0.248783 + 0.430905i
\(336\) 0 0
\(337\) 1.27189 0.0692842 0.0346421 0.999400i \(-0.488971\pi\)
0.0346421 + 0.999400i \(0.488971\pi\)
\(338\) −3.67891 + 16.1824i −0.200106 + 0.880208i
\(339\) 6.17495 + 10.6953i 0.335377 + 0.580890i
\(340\) −1.59738 0.922245i −0.0866298 0.0500158i
\(341\) −5.74305 −0.311004
\(342\) 6.12937 10.6164i 0.331438 0.574068i
\(343\) 0 0
\(344\) 23.8572 + 13.7740i 1.28630 + 0.742643i
\(345\) −12.8479 + 7.41777i −0.691710 + 0.399359i
\(346\) 5.96682 3.44494i 0.320778 0.185201i
\(347\) 25.8833 1.38949 0.694744 0.719257i \(-0.255518\pi\)
0.694744 + 0.719257i \(0.255518\pi\)
\(348\) −1.52101 −0.0815344
\(349\) 14.9967 8.65837i 0.802757 0.463472i −0.0416774 0.999131i \(-0.513270\pi\)
0.844434 + 0.535659i \(0.179937\pi\)
\(350\) 0 0
\(351\) −19.4002 2.17744i −1.03551 0.116223i
\(352\) −2.87074 + 4.97227i −0.153011 + 0.265023i
\(353\) −21.9533 12.6747i −1.16846 0.674608i −0.215140 0.976583i \(-0.569021\pi\)
−0.953316 + 0.301975i \(0.902354\pi\)
\(354\) 2.29153 3.96904i 0.121793 0.210952i
\(355\) −2.46711 4.27317i −0.130941 0.226796i
\(356\) 5.94983i 0.315341i
\(357\) 0 0
\(358\) −13.5886 7.84539i −0.718181 0.414642i
\(359\) 4.56434 + 2.63522i 0.240897 + 0.139082i 0.615589 0.788068i \(-0.288918\pi\)
−0.374692 + 0.927149i \(0.622252\pi\)
\(360\) 8.98417 0.473507
\(361\) 7.72804 13.3854i 0.406739 0.704493i
\(362\) 27.8961i 1.46618i
\(363\) 3.83077 0.201063
\(364\) 0 0
\(365\) −13.9240 −0.728813
\(366\) 1.61287i 0.0843058i
\(367\) 12.6588 21.9257i 0.660783 1.14451i −0.319627 0.947544i \(-0.603557\pi\)
0.980410 0.196967i \(-0.0631092\pi\)
\(368\) 21.8515 1.13909
\(369\) −9.02073 5.20812i −0.469601 0.271124i
\(370\) 3.49722 + 2.01912i 0.181812 + 0.104969i
\(371\) 0 0
\(372\) 0.894130i 0.0463585i
\(373\) 3.39391 + 5.87842i 0.175730 + 0.304373i 0.940414 0.340033i \(-0.110438\pi\)
−0.764684 + 0.644406i \(0.777105\pi\)
\(374\) −4.86631 + 8.42869i −0.251631 + 0.435837i
\(375\) −12.3104 7.10739i −0.635704 0.367024i
\(376\) −10.0754 + 17.4511i −0.519598 + 0.899970i
\(377\) 5.07464 + 11.6176i 0.261357 + 0.598336i
\(378\) 0 0
\(379\) 10.6717 6.16130i 0.548168 0.316485i −0.200215 0.979752i \(-0.564164\pi\)
0.748383 + 0.663267i \(0.230831\pi\)
\(380\) 3.94577 0.202414
\(381\) −13.1620 −0.674310
\(382\) 3.04815 1.75985i 0.155957 0.0900417i
\(383\) −6.28662 + 3.62958i −0.321232 + 0.185463i −0.651941 0.758269i \(-0.726045\pi\)
0.330710 + 0.943732i \(0.392712\pi\)
\(384\) 7.28815 + 4.20782i 0.371922 + 0.214729i
\(385\) 0 0
\(386\) 8.29086 14.3602i 0.421994 0.730915i
\(387\) 14.8935 0.757082
\(388\) 4.56346 + 2.63472i 0.231675 + 0.133757i
\(389\) −3.57406 6.19045i −0.181212 0.313868i 0.761082 0.648656i \(-0.224669\pi\)
−0.942293 + 0.334788i \(0.891335\pi\)
\(390\) 3.90522 + 8.94038i 0.197749 + 0.452714i
\(391\) −19.2052 −0.971250
\(392\) 0 0
\(393\) 1.78974 + 3.09991i 0.0902802 + 0.156370i
\(394\) 12.1441 + 21.0342i 0.611811 + 1.05969i
\(395\) −24.7388 + 14.2829i −1.24474 + 0.718652i
\(396\) 1.68357i 0.0846027i
\(397\) −19.4520 + 11.2306i −0.976266 + 0.563647i −0.901141 0.433527i \(-0.857269\pi\)
−0.0751252 + 0.997174i \(0.523936\pi\)
\(398\) 25.5718i 1.28180i
\(399\) 0 0
\(400\) 2.66347 + 4.61327i 0.133174 + 0.230663i
\(401\) 3.05473i 0.152546i −0.997087 0.0762729i \(-0.975698\pi\)
0.997087 0.0762729i \(-0.0243020\pi\)
\(402\) 3.74072 + 6.47912i 0.186570 + 0.323149i
\(403\) −6.82944 + 2.98315i −0.340199 + 0.148601i
\(404\) 0.0135417 0.0234549i 0.000673725 0.00116693i
\(405\) −2.22527 + 1.28476i −0.110575 + 0.0638403i
\(406\) 0 0
\(407\) −2.42149 + 4.19414i −0.120029 + 0.207896i
\(408\) −8.39817 4.84869i −0.415771 0.240046i
\(409\) 5.60586i 0.277192i 0.990349 + 0.138596i \(0.0442590\pi\)
−0.990349 + 0.138596i \(0.955741\pi\)
\(410\) 14.7513i 0.728514i
\(411\) 22.1336 + 12.7789i 1.09177 + 0.630335i
\(412\) 2.39261 4.14412i 0.117875 0.204166i
\(413\) 0 0
\(414\) 12.6586 7.30844i 0.622136 0.359190i
\(415\) −7.23597 + 12.5331i −0.355200 + 0.615224i
\(416\) −0.831013 + 7.40403i −0.0407437 + 0.363012i
\(417\) 6.46487 + 11.1975i 0.316586 + 0.548343i
\(418\) 20.8202i 1.01835i
\(419\) 3.06969 + 5.31687i 0.149964 + 0.259746i 0.931214 0.364473i \(-0.118751\pi\)
−0.781250 + 0.624219i \(0.785417\pi\)
\(420\) 0 0
\(421\) 1.92589i 0.0938622i −0.998898 0.0469311i \(-0.985056\pi\)
0.998898 0.0469311i \(-0.0149441\pi\)
\(422\) 11.0557 6.38302i 0.538184 0.310720i
\(423\) 10.8943i 0.529700i
\(424\) −27.4841 + 15.8679i −1.33475 + 0.770615i
\(425\) −2.34092 4.05459i −0.113551 0.196677i
\(426\) −2.02675 3.51044i −0.0981965 0.170081i
\(427\) 0 0
\(428\) 1.48470 0.0717658
\(429\) −10.7220 + 4.68345i −0.517664 + 0.226119i
\(430\) −10.5460 18.2662i −0.508572 0.880873i
\(431\) −9.30923 5.37469i −0.448410 0.258890i 0.258749 0.965945i \(-0.416690\pi\)
−0.707158 + 0.707055i \(0.750023\pi\)
\(432\) 16.9041 0.813301
\(433\) −20.1328 + 34.8710i −0.967520 + 1.67579i −0.264835 + 0.964294i \(0.585318\pi\)
−0.702685 + 0.711501i \(0.748016\pi\)
\(434\) 0 0
\(435\) 6.45439 + 3.72644i 0.309464 + 0.178669i
\(436\) −0.637000 + 0.367772i −0.0305068 + 0.0176131i
\(437\) 35.5799 20.5421i 1.70202 0.982662i
\(438\) −11.4386 −0.546559
\(439\) −21.9508 −1.04765 −0.523826 0.851825i \(-0.675496\pi\)
−0.523826 + 0.851825i \(0.675496\pi\)
\(440\) 13.2144 7.62934i 0.629972 0.363715i
\(441\) 0 0
\(442\) −1.40868 + 12.5509i −0.0670042 + 0.596984i
\(443\) 13.9482 24.1589i 0.662697 1.14783i −0.317207 0.948356i \(-0.602745\pi\)
0.979904 0.199469i \(-0.0639217\pi\)
\(444\) −0.652982 0.376999i −0.0309892 0.0178916i
\(445\) 14.5770 25.2481i 0.691017 1.19688i
\(446\) −5.35046 9.26727i −0.253352 0.438818i
\(447\) 2.69484i 0.127461i
\(448\) 0 0
\(449\) 19.1056 + 11.0306i 0.901648 + 0.520567i 0.877734 0.479147i \(-0.159054\pi\)
0.0239134 + 0.999714i \(0.492387\pi\)
\(450\) 3.08590 + 1.78165i 0.145471 + 0.0839876i
\(451\) −17.6909 −0.833033
\(452\) 1.95826 3.39181i 0.0921088 0.159537i
\(453\) 24.0777i 1.13127i
\(454\) 1.17408 0.0551023
\(455\) 0 0
\(456\) 20.7448 0.971464
\(457\) 5.51628i 0.258041i 0.991642 + 0.129020i \(0.0411833\pi\)
−0.991642 + 0.129020i \(0.958817\pi\)
\(458\) −15.7150 + 27.2192i −0.734314 + 1.27187i
\(459\) −14.8570 −0.693466
\(460\) 4.07447 + 2.35240i 0.189973 + 0.109681i
\(461\) −25.0092 14.4391i −1.16479 0.672494i −0.212346 0.977195i \(-0.568110\pi\)
−0.952448 + 0.304700i \(0.901444\pi\)
\(462\) 0 0
\(463\) 14.2284i 0.661251i 0.943762 + 0.330625i \(0.107260\pi\)
−0.943762 + 0.330625i \(0.892740\pi\)
\(464\) −5.48874 9.50678i −0.254808 0.441341i
\(465\) −2.19061 + 3.79424i −0.101587 + 0.175954i
\(466\) −19.1003 11.0276i −0.884804 0.510842i
\(467\) 2.27163 3.93457i 0.105118 0.182070i −0.808668 0.588265i \(-0.799811\pi\)
0.913787 + 0.406195i \(0.133145\pi\)
\(468\) 0.874509 + 2.00205i 0.0404242 + 0.0925448i
\(469\) 0 0
\(470\) 13.3613 7.71416i 0.616312 0.355828i
\(471\) −3.38288 −0.155875
\(472\) −9.30163 −0.428142
\(473\) 21.9062 12.6476i 1.00725 0.581536i
\(474\) −20.3231 + 11.7335i −0.933469 + 0.538939i
\(475\) 8.67366 + 5.00774i 0.397975 + 0.229771i
\(476\) 0 0
\(477\) −8.57886 + 14.8590i −0.392799 + 0.680348i
\(478\) −18.4883 −0.845633
\(479\) −1.44239 0.832764i −0.0659044 0.0380499i 0.466686 0.884423i \(-0.345448\pi\)
−0.532590 + 0.846373i \(0.678781\pi\)
\(480\) 2.19001 + 3.79321i 0.0999598 + 0.173135i
\(481\) −0.700965 + 6.24535i −0.0319612 + 0.284763i
\(482\) 10.7671 0.490426
\(483\) 0 0
\(484\) −0.607426 1.05209i −0.0276103 0.0478224i
\(485\) −12.9100 22.3608i −0.586215 1.01535i
\(486\) 16.1295 9.31239i 0.731650 0.422418i
\(487\) 1.48493i 0.0672884i 0.999434 + 0.0336442i \(0.0107113\pi\)
−0.999434 + 0.0336442i \(0.989289\pi\)
\(488\) −2.83487 + 1.63671i −0.128328 + 0.0740904i
\(489\) 27.3691i 1.23767i
\(490\) 0 0
\(491\) 7.99791 + 13.8528i 0.360941 + 0.625167i 0.988116 0.153711i \(-0.0491224\pi\)
−0.627175 + 0.778878i \(0.715789\pi\)
\(492\) 2.75428i 0.124173i
\(493\) 4.82404 + 8.35548i 0.217264 + 0.376312i
\(494\) −10.8148 24.7587i −0.486580 1.11395i
\(495\) 4.12473 7.14425i 0.185393 0.321110i
\(496\) 5.58860 3.22658i 0.250936 0.144878i
\(497\) 0 0
\(498\) −5.94440 + 10.2960i −0.266375 + 0.461375i
\(499\) 15.3459 + 8.85997i 0.686977 + 0.396627i 0.802479 0.596681i \(-0.203514\pi\)
−0.115501 + 0.993307i \(0.536847\pi\)
\(500\) 4.50793i 0.201601i
\(501\) 8.87852i 0.396663i
\(502\) 16.2211 + 9.36527i 0.723984 + 0.417993i
\(503\) −0.598451 + 1.03655i −0.0266836 + 0.0462174i −0.879059 0.476713i \(-0.841828\pi\)
0.852375 + 0.522931i \(0.175161\pi\)
\(504\) 0 0
\(505\) −0.114929 + 0.0663540i −0.00511425 + 0.00295272i
\(506\) 12.4126 21.4993i 0.551809 0.955760i
\(507\) −10.3175 + 11.1388i −0.458217 + 0.494692i
\(508\) 2.08703 + 3.61485i 0.0925971 + 0.160383i
\(509\) 6.28614i 0.278628i −0.990248 0.139314i \(-0.955510\pi\)
0.990248 0.139314i \(-0.0444898\pi\)
\(510\) 3.71237 + 6.43002i 0.164387 + 0.284726i
\(511\) 0 0
\(512\) 25.3457i 1.12013i
\(513\) 27.5244 15.8912i 1.21523 0.701614i
\(514\) 37.4398i 1.65140i
\(515\) −20.3061 + 11.7237i −0.894792 + 0.516608i
\(516\) 1.96909 + 3.41056i 0.0866843 + 0.150142i
\(517\) 9.25143 + 16.0240i 0.406878 + 0.704733i
\(518\) 0 0
\(519\) 6.30354 0.276695
\(520\) 11.7512 15.9366i 0.515323 0.698866i
\(521\) −5.42367 9.39407i −0.237615 0.411562i 0.722414 0.691460i \(-0.243032\pi\)
−0.960029 + 0.279899i \(0.909699\pi\)
\(522\) −6.35926 3.67152i −0.278337 0.160698i
\(523\) −1.34726 −0.0589114 −0.0294557 0.999566i \(-0.509377\pi\)
−0.0294557 + 0.999566i \(0.509377\pi\)
\(524\) 0.567579 0.983076i 0.0247948 0.0429459i
\(525\) 0 0
\(526\) −22.0167 12.7113i −0.959974 0.554241i
\(527\) −4.91181 + 2.83583i −0.213962 + 0.123531i
\(528\) 8.77394 5.06563i 0.381837 0.220453i
\(529\) 25.9873 1.12988
\(530\) 24.2984 1.05546
\(531\) −4.35510 + 2.51442i −0.188995 + 0.109117i
\(532\) 0 0
\(533\) −21.0375 + 9.18931i −0.911233 + 0.398033i
\(534\) 11.9751 20.7415i 0.518214 0.897574i
\(535\) −6.30034 3.63750i −0.272388 0.157263i
\(536\) 7.59205 13.1498i 0.327926 0.567985i
\(537\) −7.17773 12.4322i −0.309742 0.536489i
\(538\) 28.4993i 1.22869i
\(539\) 0 0
\(540\) 3.15198 + 1.81980i 0.135640 + 0.0783115i
\(541\) 17.4565 + 10.0785i 0.750516 + 0.433310i 0.825880 0.563846i \(-0.190679\pi\)
−0.0753646 + 0.997156i \(0.524012\pi\)
\(542\) −11.9996 −0.515425
\(543\) −12.7610 + 22.1027i −0.547628 + 0.948519i
\(544\) 5.67012i 0.243104i
\(545\) 3.60415 0.154385
\(546\) 0 0
\(547\) −3.42286 −0.146351 −0.0731755 0.997319i \(-0.523313\pi\)
−0.0731755 + 0.997319i \(0.523313\pi\)
\(548\) 8.10512i 0.346234i
\(549\) −0.884873 + 1.53264i −0.0377654 + 0.0654117i
\(550\) 6.05188 0.258053
\(551\) −17.8742 10.3197i −0.761467 0.439633i
\(552\) 21.4214 + 12.3677i 0.911757 + 0.526403i
\(553\) 0 0
\(554\) 18.3093i 0.777889i
\(555\) 1.84729 + 3.19960i 0.0784130 + 0.135815i
\(556\) 2.05020 3.55106i 0.0869480 0.150598i
\(557\) 20.4948 + 11.8327i 0.868394 + 0.501367i 0.866814 0.498631i \(-0.166164\pi\)
0.00157977 + 0.999999i \(0.499497\pi\)
\(558\) 2.15832 3.73832i 0.0913690 0.158256i
\(559\) 19.4806 26.4190i 0.823940 1.11740i
\(560\) 0 0
\(561\) −7.71139 + 4.45217i −0.325575 + 0.187971i
\(562\) −0.126178 −0.00532248
\(563\) 28.8075 1.21409 0.607045 0.794668i \(-0.292355\pi\)
0.607045 + 0.794668i \(0.292355\pi\)
\(564\) −2.49475 + 1.44035i −0.105048 + 0.0606496i
\(565\) −16.6198 + 9.59543i −0.699199 + 0.403683i
\(566\) 0.686177 + 0.396164i 0.0288422 + 0.0166520i
\(567\) 0 0
\(568\) −4.11343 + 7.12467i −0.172596 + 0.298945i
\(569\) 27.6722 1.16008 0.580040 0.814588i \(-0.303037\pi\)
0.580040 + 0.814588i \(0.303037\pi\)
\(570\) −13.7552 7.94158i −0.576143 0.332636i
\(571\) 6.48273 + 11.2284i 0.271294 + 0.469895i 0.969193 0.246301i \(-0.0792151\pi\)
−0.697899 + 0.716196i \(0.745882\pi\)
\(572\) 2.98641 + 2.20209i 0.124868 + 0.0920741i
\(573\) 3.22016 0.134524
\(574\) 0 0
\(575\) 5.97105 + 10.3422i 0.249010 + 0.431298i
\(576\) −7.26525 12.5838i −0.302719 0.524324i
\(577\) 8.19301 4.73023i 0.341079 0.196922i −0.319670 0.947529i \(-0.603572\pi\)
0.660749 + 0.750607i \(0.270239\pi\)
\(578\) 12.0899i 0.502875i
\(579\) 13.1381 7.58529i 0.546001 0.315234i
\(580\) 2.36354i 0.0981405i
\(581\) 0 0
\(582\) −10.6057 18.3696i −0.439620 0.761444i
\(583\) 29.1406i 1.20688i
\(584\) 11.6077 + 20.1052i 0.480332 + 0.831959i
\(585\) 1.19401 10.6382i 0.0493664 0.439837i
\(586\) 15.8892 27.5209i 0.656377 1.13688i
\(587\) 18.6673 10.7776i 0.770481 0.444837i −0.0625654 0.998041i \(-0.519928\pi\)
0.833046 + 0.553204i \(0.186595\pi\)
\(588\) 0 0
\(589\) 6.06647 10.5074i 0.249965 0.432951i
\(590\) 6.16761 + 3.56087i 0.253917 + 0.146599i
\(591\) 22.2212i 0.914059i
\(592\) 5.44180i 0.223657i
\(593\) −3.44015 1.98617i −0.141270 0.0815622i 0.427699 0.903921i \(-0.359324\pi\)
−0.568969 + 0.822359i \(0.692658\pi\)
\(594\) 9.60231 16.6317i 0.393988 0.682407i
\(595\) 0 0
\(596\) 0.740117 0.427307i 0.0303164 0.0175032i
\(597\) 11.6978 20.2612i 0.478759 0.829234i
\(598\) 3.59317 32.0138i 0.146936 1.30914i
\(599\) 9.75246 + 16.8918i 0.398475 + 0.690179i 0.993538 0.113500i \(-0.0362063\pi\)
−0.595063 + 0.803679i \(0.702873\pi\)
\(600\) 6.02997i 0.246172i
\(601\) −13.4368 23.2733i −0.548100 0.949336i −0.998405 0.0564616i \(-0.982018\pi\)
0.450305 0.892875i \(-0.351315\pi\)
\(602\) 0 0
\(603\) 8.20914i 0.334302i
\(604\) −6.61276 + 3.81788i −0.269070 + 0.155347i
\(605\) 5.95274i 0.242013i
\(606\) −0.0944146 + 0.0545103i −0.00383533 + 0.00221433i
\(607\) 12.5102 + 21.6682i 0.507772 + 0.879487i 0.999960 + 0.00899773i \(0.00286411\pi\)
−0.492187 + 0.870489i \(0.663803\pi\)
\(608\) −6.06482 10.5046i −0.245961 0.426016i
\(609\) 0 0
\(610\) 2.50628 0.101476
\(611\) 19.3249 + 14.2496i 0.781803 + 0.576478i
\(612\) 0.831324 + 1.43990i 0.0336043 + 0.0582043i
\(613\) 18.4970 + 10.6793i 0.747088 + 0.431332i 0.824641 0.565657i \(-0.191377\pi\)
−0.0775527 + 0.996988i \(0.524711\pi\)
\(614\) 12.6350 0.509908
\(615\) −6.74796 + 11.6878i −0.272104 + 0.471298i
\(616\) 0 0
\(617\) −28.5425 16.4790i −1.14908 0.663420i −0.200415 0.979711i \(-0.564229\pi\)
−0.948662 + 0.316291i \(0.897562\pi\)
\(618\) −16.6816 + 9.63111i −0.671031 + 0.387420i
\(619\) −42.3588 + 24.4559i −1.70254 + 0.982965i −0.759375 + 0.650654i \(0.774495\pi\)
−0.943170 + 0.332311i \(0.892172\pi\)
\(620\) 1.38941 0.0558002
\(621\) 37.8962 1.52072
\(622\) 8.00176 4.61982i 0.320841 0.185238i
\(623\) 0 0
\(624\) 7.80240 10.5814i 0.312346 0.423595i
\(625\) 6.77880 11.7412i 0.271152 0.469649i
\(626\) 36.1075 + 20.8467i 1.44315 + 0.833201i
\(627\) 9.52417 16.4964i 0.380359 0.658801i
\(628\) 0.536406 + 0.929083i 0.0214049 + 0.0370744i
\(629\) 4.78278i 0.190702i
\(630\) 0 0
\(631\) 4.65076 + 2.68512i 0.185144 + 0.106893i 0.589707 0.807617i \(-0.299243\pi\)
−0.404563 + 0.914510i \(0.632576\pi\)
\(632\) 41.2470 + 23.8140i 1.64072 + 0.947270i
\(633\) 11.6796 0.464223
\(634\) 10.9621 18.9869i 0.435360 0.754066i
\(635\) 20.4528i 0.811645i
\(636\) −4.53687 −0.179899
\(637\) 0 0
\(638\) −12.4714 −0.493747
\(639\) 4.44778i 0.175951i
\(640\) −6.53865 + 11.3253i −0.258463 + 0.447671i
\(641\) −39.7020 −1.56813 −0.784066 0.620677i \(-0.786858\pi\)
−0.784066 + 0.620677i \(0.786858\pi\)
\(642\) −5.17578 2.98824i −0.204272 0.117936i
\(643\) −27.8388 16.0727i −1.09785 0.633847i −0.162198 0.986758i \(-0.551858\pi\)
−0.935657 + 0.352911i \(0.885192\pi\)
\(644\) 0 0
\(645\) 19.2970i 0.759818i
\(646\) −10.2807 17.8067i −0.404489 0.700596i
\(647\) 9.92502 17.1906i 0.390193 0.675833i −0.602282 0.798283i \(-0.705742\pi\)
0.992475 + 0.122450i \(0.0390751\pi\)
\(648\) 3.71020 + 2.14209i 0.145751 + 0.0841491i
\(649\) −4.27048 + 7.39669i −0.167631 + 0.290346i
\(650\) 7.19670 3.14357i 0.282278 0.123301i
\(651\) 0 0
\(652\) 7.51671 4.33977i 0.294377 0.169959i
\(653\) −19.0005 −0.743547 −0.371773 0.928324i \(-0.621250\pi\)
−0.371773 + 0.928324i \(0.621250\pi\)
\(654\) 2.96083 0.115778
\(655\) −4.81705 + 2.78112i −0.188218 + 0.108667i
\(656\) 17.2152 9.93918i 0.672139 0.388060i
\(657\) 10.8697 + 6.27562i 0.424067 + 0.244835i
\(658\) 0 0
\(659\) 3.60729 6.24801i 0.140520 0.243388i −0.787173 0.616733i \(-0.788456\pi\)
0.927693 + 0.373345i \(0.121789\pi\)
\(660\) 2.18134 0.0849085
\(661\) 14.5068 + 8.37548i 0.564248 + 0.325769i 0.754849 0.655899i \(-0.227710\pi\)
−0.190601 + 0.981668i \(0.561044\pi\)
\(662\) −12.7235 22.0377i −0.494512 0.856520i
\(663\) −6.85751 + 9.29995i −0.266324 + 0.361180i
\(664\) 24.1291 0.936393
\(665\) 0 0
\(666\) −1.82006 3.15244i −0.0705259 0.122155i
\(667\) −12.3048 21.3126i −0.476444 0.825226i
\(668\) −2.43842 + 1.40782i −0.0943453 + 0.0544703i
\(669\) 9.79025i 0.378513i
\(670\) −10.0681 + 5.81281i −0.388964 + 0.224569i
\(671\) 3.00573i 0.116035i
\(672\) 0 0
\(673\) −18.6684 32.3346i −0.719614 1.24641i −0.961153 0.276016i \(-0.910986\pi\)
0.241539 0.970391i \(-0.422348\pi\)
\(674\) 1.62365i 0.0625406i
\(675\) 4.61916 + 8.00061i 0.177791 + 0.307944i
\(676\) 4.69519 + 1.06740i 0.180584 + 0.0410540i
\(677\) 14.0671 24.3649i 0.540641 0.936418i −0.458226 0.888836i \(-0.651515\pi\)
0.998867 0.0475826i \(-0.0151517\pi\)
\(678\) −13.6533 + 7.88271i −0.524350 + 0.302734i
\(679\) 0 0
\(680\) 7.53452 13.0502i 0.288935 0.500451i
\(681\) 0.930253 + 0.537082i 0.0356474 + 0.0205810i
\(682\) 7.33137i 0.280733i
\(683\) 2.07032i 0.0792186i 0.999215 + 0.0396093i \(0.0126113\pi\)
−0.999215 + 0.0396093i \(0.987389\pi\)
\(684\) −3.08025 1.77838i −0.117776 0.0679982i
\(685\) −19.8574 + 34.3941i −0.758714 + 1.31413i
\(686\) 0 0
\(687\) −24.9028 + 14.3776i −0.950100 + 0.548540i
\(688\) −14.2114 + 24.6149i −0.541805 + 0.938434i
\(689\) 15.1367 + 34.6531i 0.576662 + 1.32018i
\(690\) −9.46925 16.4012i −0.360488 0.624384i
\(691\) 35.8583i 1.36411i −0.731299 0.682057i \(-0.761086\pi\)
0.731299 0.682057i \(-0.238914\pi\)
\(692\) −0.999521 1.73122i −0.0379961 0.0658112i
\(693\) 0 0
\(694\) 33.0417i 1.25425i
\(695\) −17.4001 + 10.0460i −0.660023 + 0.381065i
\(696\) 12.4262i 0.471015i
\(697\) −15.1304 + 8.73552i −0.573103 + 0.330881i
\(698\) 11.0530 + 19.1443i 0.418361 + 0.724622i
\(699\) −10.0891 17.4748i −0.381604 0.660958i
\(700\) 0 0
\(701\) −44.8940 −1.69562 −0.847812 0.530297i \(-0.822081\pi\)
−0.847812 + 0.530297i \(0.822081\pi\)
\(702\) 2.77965 24.7657i 0.104911 0.934719i
\(703\) −5.11571 8.86067i −0.192943 0.334187i
\(704\) −21.3722 12.3393i −0.805497 0.465054i
\(705\) 14.1153 0.531614
\(706\) 16.1801 28.0248i 0.608947 1.05473i
\(707\) 0 0
\(708\) −1.15158 0.664867i −0.0432792 0.0249872i
\(709\) 14.0864 8.13279i 0.529026 0.305433i −0.211594 0.977358i \(-0.567865\pi\)
0.740620 + 0.671924i \(0.234532\pi\)
\(710\) 5.45497 3.14943i 0.204721 0.118196i
\(711\) 25.7496 0.965687
\(712\) −48.6087 −1.82169
\(713\) 12.5287 7.23344i 0.469203 0.270894i
\(714\) 0 0
\(715\) −7.27775 16.6613i −0.272173 0.623096i
\(716\) −2.27627 + 3.94262i −0.0850683 + 0.147343i
\(717\) −14.6487 8.45743i −0.547066 0.315849i
\(718\) −3.36403 + 5.82667i −0.125544 + 0.217449i
\(719\) 5.00744 + 8.67314i 0.186746 + 0.323454i 0.944164 0.329477i \(-0.106873\pi\)
−0.757417 + 0.652931i \(0.773539\pi\)
\(720\) 9.26949i 0.345454i
\(721\) 0 0
\(722\) 17.0873 + 9.86534i 0.635922 + 0.367150i
\(723\) 8.53100 + 4.92538i 0.317271 + 0.183177i
\(724\) 8.09380 0.300804
\(725\) 2.99966 5.19556i 0.111405 0.192958i
\(726\) 4.89022i 0.181493i
\(727\) −34.5299 −1.28064 −0.640322 0.768106i \(-0.721199\pi\)
−0.640322 + 0.768106i \(0.721199\pi\)
\(728\) 0 0
\(729\) 21.2872 0.788415
\(730\) 17.7748i 0.657875i
\(731\) 12.4904 21.6340i 0.461973 0.800161i
\(732\) −0.467959 −0.0172963
\(733\) 28.6966 + 16.5680i 1.05993 + 0.611953i 0.925414 0.378958i \(-0.123717\pi\)
0.134520 + 0.990911i \(0.457051\pi\)
\(734\) 27.9895 + 16.1598i 1.03311 + 0.596468i
\(735\) 0 0
\(736\) 14.4629i 0.533111i
\(737\) −6.97119 12.0745i −0.256787 0.444768i
\(738\) 6.64850 11.5155i 0.244735 0.423893i
\(739\) 3.47767 + 2.00784i 0.127928 + 0.0738594i 0.562598 0.826730i \(-0.309802\pi\)
−0.434670 + 0.900590i \(0.643135\pi\)
\(740\) 0.585830 1.01469i 0.0215356 0.0373007i
\(741\) 2.75703 24.5641i 0.101282 0.902386i
\(742\) 0 0
\(743\) 10.8361 6.25622i 0.397538 0.229519i −0.287883 0.957666i \(-0.592952\pi\)
0.685421 + 0.728147i \(0.259618\pi\)
\(744\) 7.30482 0.267808
\(745\) −4.18759 −0.153421
\(746\) −7.50418 + 4.33254i −0.274748 + 0.158626i
\(747\) 11.2975 6.52260i 0.413353 0.238650i
\(748\) 2.44551 + 1.41192i 0.0894168 + 0.0516248i
\(749\) 0 0
\(750\) 9.07304 15.7150i 0.331300 0.573829i
\(751\) −37.5158 −1.36897 −0.684486 0.729026i \(-0.739973\pi\)
−0.684486 + 0.729026i \(0.739973\pi\)
\(752\) −18.0053 10.3954i −0.656585 0.379080i
\(753\) 8.56826 + 14.8407i 0.312245 + 0.540824i
\(754\) −14.8306 + 6.47810i −0.540098 + 0.235919i
\(755\) 37.4150 1.36167
\(756\) 0 0
\(757\) 17.5223 + 30.3496i 0.636860 + 1.10307i 0.986118 + 0.166047i \(0.0531004\pi\)
−0.349258 + 0.937027i \(0.613566\pi\)
\(758\) 7.86530 + 13.6231i 0.285680 + 0.494813i
\(759\) 19.6697 11.3563i 0.713963 0.412207i
\(760\) 32.2360i 1.16932i
\(761\) −3.72586 + 2.15113i −0.135062 + 0.0779782i −0.566009 0.824399i \(-0.691513\pi\)
0.430946 + 0.902378i \(0.358180\pi\)
\(762\) 16.8021i 0.608677i
\(763\) 0 0
\(764\) −0.510605 0.884394i −0.0184730 0.0319962i
\(765\) 8.14693i 0.294553i
\(766\) −4.63340 8.02528i −0.167411 0.289965i
\(767\) −1.23621 + 11.0141i −0.0446368 + 0.397698i
\(768\) 5.00195 8.66363i 0.180492 0.312622i
\(769\) −10.6146 + 6.12834i −0.382772 + 0.220994i −0.679024 0.734116i \(-0.737597\pi\)
0.296251 + 0.955110i \(0.404263\pi\)
\(770\) 0 0
\(771\) −17.1268 + 29.6645i −0.616806 + 1.06834i
\(772\) −4.16649 2.40552i −0.149955 0.0865767i
\(773\) 3.80327i 0.136794i −0.997658 0.0683970i \(-0.978212\pi\)
0.997658 0.0683970i \(-0.0217884\pi\)
\(774\) 19.0126i 0.683393i
\(775\) 3.05424 + 1.76336i 0.109711 + 0.0633419i
\(776\) −21.5250 + 37.2824i −0.772702 + 1.33836i
\(777\) 0 0
\(778\) 7.90250 4.56251i 0.283318 0.163574i
\(779\) 18.6872 32.3672i 0.669538 1.15967i
\(780\) 2.59398 1.13307i 0.0928792 0.0405703i
\(781\)